When Hale enters as a character in The Crucible, he comes to assist in finding the "evil spirits" loose in Salem. When Giles Corey asks Hale to look into his wife reading "strange books," Hale promises he will. Later, Hale comes to the Proctor household to question the Proctors' Christian character, also informing them that he has just come from the Nurse household. After the Proctors' disbelief, Hale reminds them that, until the devil's fall, "God thought him beautiful in heaven" (Act II). When the court officials come to take accused women such as Martha Corey and Elizabeth Proctor, Hale promises he will stand up for the accused "if they are innocent," to which John Proctor responds, "If they are innocent!" (Act II). Throughout the play, Hale's intentions are good, but he comes originally as someone from out of town (Beverly, specifically) to assist Reverend Parris and court officials. It is only at the end of Act III, when Hale renounces his connection to the Salem courts, that he begins literally to speak out against the happenings in town.

All of these events, plus condemnations of other innocent Salemites, contribute to Hale's outburst in Act IV that there is "blood on [his] hands!" Hale feels guilty that he has, in a way, contributed to the arrests of so many innocent victims, and he wants to rectify his wrongs by trying to get Proctor to "confess" his wrongdoings, even if it is a lie. Hale knows, by this point, that Salem has lost many innocent souls, and he doesn't want John Proctor's soul on his conscience. Though Hale has not literally killed anyone, he definitely does feel like he has contributed to the hysteria that resulted in many unjustified deaths.

I hope this answer helps. Once I can get my hands on a hard copy of the play, I can edit this answer to include specific line numbers and more detailed quotes, if you'd like.

In act four, we see that Hale has experienced a change of heart. In the first three acts, he was a part of the sentencing of many women, and a part of a lot of the questioning, condemning, and accusations that were a part of the witch trials. But in act three, as John, Giles and Franics attempt over and over to prove the accusations false, and to valiantly save their wives and friends, Hale is touched. He is especially moved by John's willingness to besmirch his reputation (regarding adultery) in order to prove Abigail Williams a cold-hearted girl seeking revenge. After John confesses, and Elizabeth lies about the affair, Hale finally jumps in and states,

"I may shut my conscience to it no more-private vengeance is working through this testimony! From the beginning this man has struck me true...I believe him!"

Later, he even goes as far as to declare, leaving, "I quit this court!" He is so disgusted with the fact that the judges believe Abby's antics that he leaves, frustrated.

In the interim between acts three and four, we are led to believe that Hale has been approaching each of the condemned prisoners and begging them to confess, so that they won't be hanged. He doesn't like this task; in fact, he calls it "the Devils work" because he "comes to counsel Christians they should belie themselves", meaning, lie about being a witch, in order to save their life. But, he feels guilty that he condemned so many people to hang, so he is trying to save as many lives as he possibly can. He feels personally responsible for their deaths. So, when he says, "There is blood on my head," he is referring to the fact that it was he himself who signed their death warrants, and so their blood, or lives, is his personal responsibility. He bears the blame, weight, or fault, of these people dying innocently, on his shoulders. Saying that there is blood on his head is just another way of him saying that he feels guilty for the death of these people. I hope that explanation helps a bit; good luck!